2019/01/28 by Jorge Delgado, Delgado, Jorge, J.M. Peña +1
Engineering · Computer Science · Mathematics · #Advanced Numerical Analysis Techniques #Matrix Theory and Algorithms #Advanced Optimization Algorithms Research
paper · pdf · doi:10.48550/arxiv.1901.09768
Totally positive matrices are related with the shape preserving representations of a space of functions. The normalized B-basis of the space has optimal shape preserving properties. B-splines and rational Bernstein bases are examples of normalized B-bases. Some results on the optimal conditioning and on extremal properties of the minimal eigenvalue and singular value of the collocation matrices of normalized B-bases are proved. Numerical examples confirm the theoretical results and answer related questions.